Chapter 1, Problem 14CT

a.

To determine

To identify : the parent function.

Answer to Problem 14CT

The parent function is $f\left(x\right)=\sqrt{x}$.

Explanation of Solution

Given information :

The function is $g\left(x\right)=\sqrt{-7x-14}$.

form the function provided in the question it can be observed that the function is transformed by the parent function of $f\left(x\right)=\sqrt{x}$.

b.

To determine

To describe : the sequence of transformations $f$ to $g$.

Answer to Problem 14CT

Stretch vertically by a factor of $7$ , reflect it in the y -axis, shift $14$ units left.

Explanation of Solution

Given information :

The function is $g\left(x\right)=\sqrt{-7x-14}$.

since parent function is $f\left(x\right)=\sqrt{x}$ ,to transform the graph form $f$ to $g$ , first shift the stretch the graph vertically by a factor of $7$ and then reflect it in the y -axis then shift $14$ units left.

c.

To determine

To draw : the graph of function g.

Explanation of Solution

Given information :

The function is $g\left(x\right)=\sqrt{-7x-14}$.

graph : first, to graph the parent function use the point plotting,

x	1	4	9	16
y	1	2	3	4

Now first shift the stretch the graph vertically by a factor of $7$ and then reflect it in the y -axis then shift $14$ units left.

Thus, the graph can be obtained as: